YEAR 3 MATHS FOCUS
NUMBERS AND ALGEBRA
Whole Numbers
Addition & Subtraction
Multiplication & Division
Fractions & Decimals
Patterns & Algebra
Whole Numbers
WHOLE NUMBERS
OUTCOME
A student:
MA2-4NA: applies place value to order, read and represent numbers of up to five digits
| Teaching Points | The place value of digits in various numerals should be investigated. Students should understand, for example, that the ‘5’ in 35 represents 5 ones, but the ‘5’ in 53 represents 50 or 5 tens. |
Language | Students should be able to communicate using the following language: number before, number after, more than, greater than, less than, largest number, smallest number, ascending order, descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to. |
| The word ‘and’ is used between the hundreds and the tens when reading and writing a number in words, but not in other places, eg 3568 is read as ‘three thousand, five hundred and sixty-eight’. | |
The word ’round’ has different meanings in different contexts, eg ‘The plate is round’, ‘Round 23 to the nearest ten’. |
Expectations of Attainment
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) | represent numbers of up to four digits using objects, words, numerals and digital displays |
| – make the largest and smallest number from four given digits (Communicating) | |
| identify the number before and after a given two-, three- or four-digit number | |
| – describe the number before as ‘one less than’ and the number after as ‘one more than’ a given number (Communicating) | |
| count forwards and backwards by tens and hundreds on and off the decade, eg 1220, 1230, 1240, … (on the decade); 423, 323, 223, … (off the decade) | |
| arrange numbers of up to four digits in ascending and descending order | |
| – use place value to compare and explain the relative size of four-digit numbers (Communicating, Reasoning) | |
| use the terms and symbols for ‘is less than’ (<) and ‘is greater than’ (>) to show the relationship between two numbers |
Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) | apply an understanding of place value and the role of zero to read, write and order numbers of up to four digits |
| – interpret four-digit numbers used in everyday contexts (Problem Solving) | |
| use place value to partition numbers of up to four digits, eg 3265 as 3 groups of one thousand, 2 groups of one hundred, 6 groups of ten and 5 ones | |
| state the ‘place value’ of digits in numbers of up to four digits, eg ‘In the number 3426, the place value of the “4” is 400 or 4 hundreds’ | |
| record numbers of up to four digits using place value, eg 5429 = 5000 + 400 + 20 + 9 | |
| partition numbers of up to four digits in non-standard forms, eg 3265 as 32 hundreds and 65 ones | |
| round numbers to the nearest ten, hundred or thousand |
Addition & Subtraction
ADDITION & SUBTRACTION
OUTCOME
A student:
MA2-5NA: uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers
Teaching Points | Students need to understand the different uses for the = sign, eg 4 + 1 = 5, where the = sign indicates that the right side of the number sentence contains ‘the answer’ and should be read to mean ‘equals’, compared to a statement of equality such as 4 + 1 = 3 + 2, where the = sign should be read to mean ‘is the same as’. |
In Stage 2, it is important that students apply and extend their repertoire of mental strategies for addition and subtraction. The use of concrete materials to model the addition and subtraction of two or more numbers, with and without trading, is intended to provide a foundation for the introduction of the formal algorithm in Addition and Subtraction 2. | |
One-cent and two-cent coins were withdrawn by the Australian Government in 1990. Prices can still be expressed in one-cent increments, but the final bill is rounded to the nearest five cents (except for electronic transactions), eg $5.36, $5.37 round to $5.35 $5.38, $5.39, $5.41, $5.42 round to $5.40 $5.43, $5.44 round to $5.45. |
| Language | Students should be able to communicate using the following language: plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, is the same as, number sentence, empty number line, strategy, digit, estimate, round to. |
Expectations of Attainment
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation(ACMNA055) | add three or more single-digit numbers |
| model and apply the associative property of addition to aid mental computation, eg 2 + 3 + 8 = 2 + 8 + 3 = 10 + 3 = 13 | |
| apply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers, including: the jump strategy on an empty number line, eg 823 + 56: 823 + 50 = 873, 873 + 6 = 879 the split strategy, eg 23 + 35: 20 + 30 + 3 + 5 = 58 the compensation strategy, eg 63 + 29: 63 + 30 = 93, subtract 1 to obtain 92 using patterns to extend number facts, eg 500 – 200: 5 – 2 = 3, so 500 – 200 = 300 bridging the decades, eg 34 + 26: 34 + 6 = 40, 40 + 20 = 60 changing the order of addends to form multiples of 10, eg 16 + 8 + 4: add 16 to 4 first using place value to partition numbers, eg 2500 + 670: 2500 + 600 + 70 = 3170 partitioning numbers in non-standard forms, eg 500 + 670: 670 = 500 + 170, so 500 + 670 = 500 + 500 + 170, which is 1000 + 170 = 1170 | |
| – choose and apply efficient strategies for addition and subtraction (Problem Solving) | |
| – discuss and compare different methods of addition and subtraction (Communicating) | |
| use concrete materials to model the addition and subtraction of two or more numbers, with and without trading, and record the method used | |
| select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to four digits | |
| – give a reasonable estimate for a problem, explain how the estimate was obtained, and check the solution (Communicating, Reasoning) | |
| use the equals sign to record equivalent number sentences involving addition and subtraction and so to mean ‘is the same as’, rather than to mean to perform an operation, eg 32 – 13 = 30 – 11 | |
| – check given number sentences to determine if they are true or false and explain why, eg ‘Is 39 – 12 = 15 + 11 true? Why or why not?’ (Communicating, Reasoning) |
Recognise and explain the connection between addition and subtraction (ACMNA054) | demonstrate how addition and subtraction are inverse operations |
| explain and check solutions to problems, including by using the inverse operation |
Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059) | calculate equivalent amounts of money using different denominations, eg 70 cents can be made up of three 20-cent coins and a 10-cent coin, or two 20-cent coins and three 10-cent coins, etc |
| perform simple calculations with money, including finding change, and round to the nearest five cents | |
| calculate mentally to give change |
Multiplication & Division
MULTIPLICATION & DIVISION
OUTCOME
A student:
MA2-6NA: uses mental and informal written strategies for multiplication and division
TEACHING POINTS | When beginning to build and read multiplication facts aloud, it is best to use a language pattern of words that relates back to concrete materials such as arrays. As students become more confident with recalling multiplication facts, they may use less language. For example, ‘five rows (or groups) of three’ becomes ‘five threes’ with the ‘rows of’ or ‘groups of’ implied. This then leads to ‘one three is three’, ‘two threes are six’, ‘three threes are nine’, and so on. |
| In Stage 2, the emphasis in multiplication and division is on students developing mental strategies and using their own (informal) methods for recording their strategies. Comparing their own method of solution with the methods of other students will lead to the identification of efficient mental and written strategies. One problem may have several acceptable methods of solution. | |
| Students could extend their recall of number facts beyond the multiplication facts to 10 × 10 by also memorising multiples of numbers such as 11, 12, 15, 20 and 25. | |
| An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations. | |
| The use of digital technologies includes the use of calculators. |
| Language | Students should be able to communicate using the following language: group, row, column, horizontal, vertical, array, multiply, multiplied by, multiplication, multiplication facts, double, shared between, divide, divided by, division, equals, strategy, digit, number chart. |
Expectations of Attainment
Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) | count by twos, threes, fives or tens using skip counting |
| use mental strategies to recall multiplication facts for multiples of two, three, five and ten | |
| – relate ‘doubling’ to multiplication facts for multiples of two, eg ‘Double three is six’ (Reasoning) | |
| recognise and use the symbols for multiplied by (×), divided by (÷) and equals (=) | |
link multiplication and division facts using groups or arrays, eg
| |
| – explain why a rectangular array can be read as a division in two ways by forming vertical or horizontal groups, eg 12 ÷ 3 = 4 or 12 ÷ 4 = 3 (Communicating, Reasoning) | |
| model and apply the commutative property of multiplication, eg 5 × 8 = 8 × 5 |
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) | use mental strategies to multiply a one-digit number by a multiple of 10, including: repeated addition, eg 3 × 20: 20 + 20 + 20 = 60 using place value concepts, eg 3 × 20: 3 × 2 tens = 6 tens = 60 factorising the multiple of 10, eg 3 × 20: 3 × 2 × 10 = 6 × 10 = 60 |
| – apply the inverse relationship of multiplication and division to justify answers, eg 12 ÷ 3 is 4 because 4 × 3 = 12 (Reasoning) | |
| select, use and record a variety of mental strategies, and appropriate digital technologies, to solve simple multiplication problems | |
| – pose multiplication problems and apply appropriate strategies to solve them (Communicating, Problem Solving)Critical and creative thinking | |
| – explain how an answer was obtained and compare their own method of solution with the methods of other students (Communicating, Reasoning) | |
| – explain problem-solving strategies using language, actions, materials and drawings (Communicating, Problem Solving) | |
| – describe methods used in solving multiplication problems (Communicating) |
Fractions & Decimals
FRACTIONS & DECIMALS
OUTCOME
A student:
MA2-7NA: represents, models and compares commonly used fractions and decimals
TEACHING POINTS | Fractions are used in different ways: to describe equal parts of a whole; to describe equal parts of a collection of objects; to denote numbers (eg 12 is midway between 0 and 1 on the number line); and as operators related to division (eg dividing a number in half) |
Three Models of Fractions
|
LANGUAGE | Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, third, fifth, one-third, one-fifth, fraction, denominator, numerator, mixed numeral, whole number, fractional part, number line. |
| When expressing fractions in English, the numerator is said first, followed by the denominator. However, in many Asian languages (eg Chinese, Japanese), the opposite is the case: the denominator is said before the numerator. |
Expectations of Attainment
Model and represent unit fractions, including 1/2, 1/4, 1/3 and 1/5 and their multiples, to a complete whole (ACMNA058) | model fractions with denominators of 2, 3, 4, 5 and 8 of whole objects, shapes and collections using concrete materials and diagrams, eg  |
| – recognise that as the number of parts that a whole is divided into becomes larger, the size of each part becomes smaller (Reasoning) | |
– recognise that fractions are used to describe one or more parts of a whole where the parts are equal, eg  | |
| name fractions up to one whole, eg 1/5, 2/5, 3/5, 4/5, 5/5 | |
| interpret the denominator as the number of equal parts a whole has been divided into | |
| interpret the numerator as the number of equal fractional parts, eg 3/8 means 3 equal parts of 8 | |
| use the terms ‘fraction’, ‘denominator’ and ‘numerator’ appropriately when referring to fractions |
Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line (ACMNA078) | identify and describe ‘mixed numerals’ as having a whole-number part and a fractional part |
| rename 2/2, 3/3, 4/4, 5/5 and 8/8 as 1 | |
| count by halves, thirds and quarters, eg 0, 1/3, 2/3, 1, 1 1/3, 1 2/3, 2, 2 1/3, … | |
place halves, quarters, eighths and thirds on number lines between 0 and 1, eg | |
place halves, thirds and quarters on number lines that extend beyond 1, eg
| |
| compare unit fractions using diagrams and number lines and by referring to the denominator, eg 1/8 is less than 1/2 | |
| – recognise and explain the relationship between the value of a unit fraction and its denominator (Communicating, Reasoning) |
Patterns & Algebra
PATTERNS & ALGEBRA
OUTCOME
A student:
MA2-8NA: generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values
| TEACHING POINTS | In Stage 2, number patterns include additive patterns that increase or decrease from any starting point. |
| LANGUAGE | Students should be able to communicate using the following language: pattern, goes up by, goes down by, even, odd, rows, digit, multiplication facts. |
Expectations of Attainment
Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060) | identify and describe patterns when counting forwards or backwards by threes, fours, sixes, sevens, eights and nines from any starting point |
| model, describe and then record number patterns using diagrams, words or symbols | |
| – ask questions about how number patterns have been created and how they can be continued (Communicating) | |
| create and continue a variety of number patterns that increase or decrease, and describe them in more than one way |
Investigate the conditions required for a number to be even or odd and identify even and odd numbers (ACMNA051) | model even and odd numbers of up to two digits using arrays with two rows |
| – compare and describe the difference between models of even numbers and models of odd numbers (Communicating) | |
| – recognise the connection between even numbers and the multiplication facts for two (Reasoning) | |
| describe and generalise the conditions for a number to be even or odd | |
| – recognise the significance of the final digit of a whole number in determining whether a given number is even or odd (Reasoning) | |
| identify even or odd numbers of up to four digits |
MEASUREMENT AND GEOMETRY
Length
Area
Volume & Capacity
Mass
Time
3D Space
2D Space
Angles
Position
Length
LENGTH
OUTCOME
A student:
MA2-9MG: measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures
Teaching Points | In Stage 2, measurement experiences enable students to develop an understanding of the size of the metre, centimetre and millimetre, to estimate and measure using these units, and to select the appropriate unit and measuring device. |
| When recording measurements, a space should be left between the number and the abbreviated unit, eg 3 cm, not 3cm. |
| LANGUAGE | Students should be able to communicate using the following language: length, distance, metre, centimetre, millimetre, ruler, measure, estimate, handspan. |
Expectations of Attainment
Measure, order and compare objects using familiar metric units of length (ACMMG061) | measure lengths and distances using metres and centimetres |
| record lengths and distances using metres and centimetres, e.g. 1 m 25 cm | |
| compare and order lengths and distances using metres and centimetres | |
| estimate lengths and distances using metres and centimetres and check by measuring | |
| – explain strategies used to estimate lengths and distances, such as by referring to a known length, eg ‘My handspan is 10 cm and my desk is 8 handspans long, so my desk is about 80 cm long’ (Communicating, Problem Solving) | |
| recognise the need for a formal unit smaller than the centimetre to measure length | |
| recognise that there are 10 millimetres in one centimetre, ie 10 millimetres = 1 centimetre | |
| use the millimetre as a unit to measure lengths to the nearest millimetre, using a ruler | |
| – describe how a length or distance was measured (Communicating) | |
| record lengths using the abbreviation for millimetres (mm), eg 5 cm 3 mm or 53 mm | |
| estimate lengths to the nearest millimetre and check by measuring |
Area
AREA
OUTCOME
A student:
MA2-10MG: measures, records, compares and estimates areas using square centimetres and square metres
TEACHING POINTS | In Stage 2, students should appreciate that formal units allow for easier and more accurate communication of measures. Measurement experiences should enable students to develop an understanding of the size of a unit, measure and estimate using the unit, and select the appropriate unit. |
| An important understanding in Stage 2 is that an area of one square metre need not be a square. It could, for example, be a rectangle two metres long and half a metre wide. |
LANGUAGE | Students should be able to communicate using the following language: area, surface, measure, grid, row, column, square centimetre, square metre, estimate. |
| The abbreviation m^2 is read as ‘square metre(s)’ and not ‘metre(s) squared’ or ‘metre(s) square’. Similarly, the abbreviation cm^2 is read as ‘square centimetre(s)’ and not ‘centimetre(s) squared’ or ‘centimetre(s) square’. |
EXPECTATIONS OF ATTAINMENT
Recognise and use formal units to measure and estimate the areas of rectangles | recognise the need for the square centimetre as a formal unit to measure area |
| use a 10 cm × 10 cm tile (or grid) to find the areas of rectangles (including squares) that are less than, greater than or about the same as 100 square centimetres | |
| measure the areas of rectangles (including squares) in square centimetres | |
| – use efficient strategies for counting large numbers of square centimetres, eg using strips of 10 or squares of 100 (Problem Solving) | |
| record area in square centimetres using words and the abbreviation for square centimetres (cm2), eg 55 square centimetres, 55 cm^2 | |
| estimate the areas of rectangles (including squares) in square centimetres | |
| – discuss strategies used to estimate area in square centimetres, eg visualising repeated units (Communicating, Problem Solving) | |
| recognise the need for a formal unit larger than the square centimetre to measure area | |
| construct a square metre and use it to measure the areas of large rectangles (including squares), eg the classroom floor or door | |
| – explain where square metres are used for measuring in everyday situations, eg floor coverings (Communicating, Problem Solving, Critical and creative thinking) | |
| – recognise areas that are ‘less than a square metre’, ‘about the same as a square metre’ and ‘greater than a square metre’ (Reasoning, Literacy) | |
| recognise that an area of one square metre need not be a square, eg cut a 1 m by 1 m square in half and join the shorter ends of each part together to create an area of one square metre that is rectangular (two metres by half a metre) (Problem Solving, Reasoning, Critical and creative thinking) | |
| record areas in square metres using words and the abbreviation for square metres (m^2), eg 6 square metres, 6 m^2 (Literacy) | |
| estimate the areas of rectangles (including squares) in square metres | |
| – discuss strategies used to estimate area in square metres, eg visualising repeated units (Communicating, Problem Solving) |
Volume & Capacity
VOLUME & CAPACITY
OUTCOME
A student:
MA2-11MG: measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres
TEACHING POINTS | Volume and capacity relate to the measurement of three-dimensional space, in the same way that area relates to the measurement of two-dimensional space and length relates to the measurement of one dimension. The attribute of volume is the amount of space occupied by an object or substance and is usually measured in cubic units, eg cubic centimetres (cm3) and cubic metres (m3). |
| Capacity refers to the amount a container can hold and is measured in units such as millilitres (mL), litres (L) and kilolitres (kL). Capacity is only used in relation to containers and generally refers to liquid measurement. The capacity of a closed container will be slightly less than its volume – capacity is based on the inside dimensions, while volume is determined by the outside dimensions of the container. It is not necessary to refer to these definitions with students (capacity is not taught as a concept separate from volume until Stage 4). | |
| In Stage 2, students should appreciate that formal units allow for easier and more accurate communication of measures. Students should be introduced to the litre, millilitre and cubic centimetre. | |
| Measurement experiences should enable students to develop an understanding of the size of a unit, to estimate and measure using the unit, and to select the appropriate unit and measuring device. | |
| Liquids are commonly measured in litres and millilitres. The capacities of containers used to hold liquids are therefore usually measured in litres and millilitres, eg a litre of milk will fill a container that has a capacity of one litre. | |
| The cubic centimetre can be related to the centimetre as a unit to measure length and the square centimetre as a unit to measure area. |
LANGUAGE | Students should be able to communicate using the following language: capacity, container, litre, volume, layers, cubic centimetre, measure, estimate. |
| The abbreviation cm^3 is read as ‘cubic centimetre(s)’ and not ‘centimetres cubed’. |
EXPECTATIONS OF ATTAINMENT
Measure, order and compare objects using familiar metric units of capacity (ACMMG061) | recognise the need for formal units to measure volume and capacity |
| – explain the need for formal units to measure volume and capacity (Communicating, Reasoning, Critical and creative thinking) | |
| use the litre as a unit to measure volumes and capacities to the nearest litre | |
| – relate the litre to familiar everyday containers, eg milk cartons (Reasoning) | |
| – recognise that one-litre containers can be a variety of shapes (Reasoning) | |
| record volumes and capacities using the abbreviation for litres (L) | |
| compare and order two or more containers by capacity measured in litres | |
| estimate the capacity of a container in litres and check by measuring | |
| – estimate the number of cups needed to fill a container with a capacity of one litre (Reasoning) |
Compare objects using familiar metric units of volume (ACMMG290) | recognise the advantages of using a cube as a unit when packing and stacking |
| use the cubic centimetre as a unit to measure volumes | |
| – pack small containers with cubic-centimetre blocks and describe packing in terms of layers, eg 2 layers of 10 cubic-centimetre blocks (Problem Solving) | |
| construct three-dimensional objects using cubic-centimetre blocks and count the blocks to determine the volumes of the objects | |
| – devise and explain strategies for counting blocks (Communicating, Problem Solving, Critical and creative thinking) | |
| record volumes using the abbreviation for cubic centimetres (cm^3) | |
| compare the volumes of two or more objects made from cubic-centimetre blocks by counting blocks | |
| distinguish between mass and volume, eg ‘This stone is heavier than the ball but it takes up less space’ (Critical and creative thinking) |
Mass
MASS
OUTCOME
A student:
MA2-12MG: measures, records, compares and estimates the masses of objects using kilograms and grams
| TEACHING POINTS | In Stage 2, students should appreciate that formal units allow for easier and more accurate communication of measures. Students are introduced to the kilogram and gram. They should develop an understanding of the size of these units, and use them to measure and estimate. |
LANGUAGE | Students should be able to communicate using the following language: mass, more than, less than, about the same as, pan balance, (level) balance, measure, estimate, kilogram. |
| Hefting’ is testing the weight of an object by lifting and balancing it. Where possible, students can compare the weights of two objects by using their bodies to balance each object, e.g. holding one object in each hand. | |
| As the terms ‘weigh’ and ‘weight’ are common in everyday usage, they can be accepted in student language should they arise (although Gabi disagrees as this caused troubles for her at university). Weight is a force that changes with gravity, while mass remains constant. |
EXPECTATIONS OF ATTAINMENT
Measure, order and compare objects using familiar metric units of mass (ACMMG061) | recognise the need for a formal unit to measure mass |
| use the kilogram as a unit to measure mass, using a pan balance | |
| – associate kilogram measures with familiar objects, eg a standard pack of flour has a mass of 1 kg, a litre of milk has a mass of approximately 1 kg {Reasoning} | |
| – recognise that objects with a mass of one kilogram can be a variety of shapes and sizes {Reasoning} | |
| record masses using the abbreviation for kilograms (kg) | |
| use hefting to identify objects that have a mass of ‘more than’, ‘less than’ and ‘about the same as’ one kilogram | |
| – discuss strategies used to estimate mass, eg by referring to a known mass {Communicating, Problem Solving} | |
| compare and order two or more objects by mass measured to the nearest kilogram | |
| estimate the number of similar objects that have a total mass of one kilogram and check by measuring | |
| explain why two students may obtain different measures for the same mass {Communicating, Reasoning, Critical and creative thinking} |
Time
TIME
OUTCOME
A student:
MA2-13MG: reads and records time in one-minute intervals and converts between hours, minutes and seconds
| TEACHING POINTS | The duration of a solar year is actually 365 days 5 hours 48 minutes and 45.7 seconds. |
| LANGUAGE | Students should be able to communicate using the following language: time, clock, analog, digital, hour hand, minute hand, second hand, revolution, numeral, hour, minute, second, o’clock, (minutes) past, (minutes) to. |
EXPECTATIONS OF ATTAINMENT
Tell time to the minute and investigate the relationship between units of time (ACMMG062) | recognise the coordinated movements of the hands on an analog clock, including: the number of minutes it takes for the minute hand to move from one numeral to the next the number of minutes it takes for the minute hand to complete one revolution the number of minutes it takes for the hour hand to move from one numeral to the next the number of minutes it takes for the minute hand to move from the 12 to any other numeral the number of seconds it takes for the second hand to complete one revolution |
| read analog and digital clocks to the minute, including using the terms ‘past’ and ‘to’, eg 7:35 is read as ‘seven thirty-five’ or ‘twenty-five to eight’ {Literacy} | |
| record in words various times shown on analog and digital clocks {Literacy} |
3D Space
THREE-DIMENSIONAL SPACE
OUTCOME
A student:
MA2-14MG: makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features
| TEACHING POINTS | The formal names for particular prisms and pyramids are not introduced in Stage 2. Prisms and pyramids are to be treated as classes for the grouping of all prisms and all pyramids. Names for particular prisms and pyramids are introduced in Stage 3. |
LANGUAGE | Students should be able to communicate using the following language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, surface, flat surface, curved surface, face, edge, vertex (vertices), net. |
| In geometry, the term ‘face’ refers to a flat surface with only straight edges, as in prisms and pyramids, eg a cube has six faces. Curved surfaces, such as those found in cylinders, cones and spheres, are not classified as ‘faces’. Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cylinders and cones, are not ‘faces’. | |
| The term ‘shape’ refers to a two-dimensional figure. The term ‘object’ refers to a three-dimensional figure. |
EXPECTATIONS OF ATTAINMENT
Make models of three-dimensional objects and describe key features (ACMMG063) | identify and name three-dimensional objects as prisms (including cubes), pyramids, cylinders, cones and spheres {Literacy} |
| – recognise and describe the use of three-dimensional objects in a variety of contexts, eg buildings, packaging {Communicating, Literacy Critical and creative thinking} | |
| describe and compare curved surfaces and flat surfaces of cylinders, cones and spheres, and faces, edges and vertices of prisms (including cubes) and pyramids {Literacy} | |
| – describe similarities and differences between prisms (including cubes), pyramids, cylinders, cones and spheres {Communicating, Literacy Critical and creative thinking} | |
| use a variety of materials to make models of prisms (including cubes), pyramids, cylinders, cones and spheres, given a three-dimensional object, picture or photograph to view | |
| deconstruct everyday packages that are prisms (including cubes) to create nets, eg cut up tissue boxes | |
| – recognise that a net requires each face to be connected to at least one other face {Reasoning, Critical and creative thinking} | |
– investigate, make and identify the variety of nets that can be used to create a particular prism, such as the variety of nets that can be used to make a cube, e.g.  {Communicating, Problem Solving, Reasoning, Literacy} | |
| – distinguish between (flat) nets, which are ‘two-dimensional’, and objects created from nets, which are ‘three-dimensional’ {Communicating, Reasoning, Literacy} |
2D Space
TWO-DIMENSIONAL SPACE
OUTCOME
A student:
MA2-15MG: manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
TEACHING POINTS | The special quadrilaterals are the parallelogram, rectangle, rhombus, square, trapezium and kite. |
| Regular shapes have all sides equal and all angles equal. In Stage 2, students are expected to be able to distinguish between regular and irregular shapes and to describe a polygon as either regular or irregular, eg a regular pentagon has five equal sides and five equal angles. | |
| It is important for students to have experiences with a variety of shapes in order to develop flexible mental images. Students need to be able to recognise shapes presented in different orientations. | |
| When constructing polygons using materials such as straws of different lengths for sides, students should be guided to an understanding that: sometimes a triangle cannot be made from 3 straws; a figure made from 3 lengths, ie a triangle, is always flat; a figure made from 4 or more lengths need not be flat; a unique triangle is formed, if a triangle can be formed, from 3 given lengths; more than one two-dimensional shape can result if more than 3 lengths are used. | |
| When using examples of Aboriginal rock carvings and other Aboriginal art, it is recommended that local examples be used wherever possible. Consult with local Aboriginal communities and education consultants for such examples. |
LANGUAGE | Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, orientation, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, symmetry, line (axis) of symmetry, rigid. |
The term ‘polygon’ (derived from the Greek words meaning ‘many angles’) refers to closed shapes with three or more angles and sides. While the angles are the focus for the general naming system used for shapes, polygons are more usually understood in terms of their sides. Students are not expected to use the term ‘polygon’. However, some students may explore other polygons and so benefit from being introduced to the collective term. Students could explore the language origins of the names of polygons. | |
| The term ‘diamond’ is often used in everyday contexts when describing quadrilaterals with four equal sides. However, ‘diamond’ is not the correct geometrical term to name such quadrilaterals; the correct term is ‘rhombus’. |
EXPECTATIONS OF ATTAINMENT
Compare and describe features of two-dimensional shapes, including the special quadrilaterals | manipulate, compare and describe features of two-dimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites {Literacy} |
| – determine the number of pairs of parallel sides, if any, of each of the special quadrilaterals {Reasoning} | |
| use measurement to establish and describe side properties of the special quadrilaterals, eg the opposite sides of a parallelogram are the same length | |
identify and name the special quadrilaterals presented in different orientations, e.g.
| |
| – explain why a particular quadrilateral has a given name, eg ‘It is a parallelogram because it has four sides and the opposite sides are parallel’ {Communicating, Reasoning, Literacy} | |
| – name a shape, given a written or verbal description of its features {Reasoning, Critical and creative thinking} | |
| recognise the vertices of two-dimensional shapes as the vertices of angles that have the sides of the shape as their arms {Literacy} | |
| identify right angles in squares and rectangles | |
| group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles | |
| identify and describe two-dimensional shapes as either ‘regular’ or ‘irregular’, eg ‘This shape is a regular pentagon because it has five equal sides and five equal angles’ {Literacy} | |
– identify regular shapes in a group that includes irregular shapes, such as a regular pentagon in a group of pentagons, e.g.
| |
| – explain the difference between regular and irregular two-dimensional shapes {Communicating, Reasoning, Literacy} | |
| – recognise that the name of a shape does not change if its size or orientation in space is changed {Reasoning} | |
| draw representations of regular and irregular two-dimensional shapes in different orientations | |
| construct regular and irregular two-dimensional shapes from a variety of materials, eg cardboard, straws, pattern blocks | |
| – determine that a triangle cannot be constructed from three straws if the sum of the lengths of the two shorter straws is less than the length of the longest straw {Reasoning} | |
| compare the rigidity of two-dimensional frames of three sides with the rigidity of those of four or more sides | |
| – construct and manipulate a four-sided frame and explain how adding a brace can make a four-sided frame rigid {Communicating, Reasoning, Critical and creative thinking} |
Identify symmetry in the environment (ACMMG066) | identify lines of symmetry in pictures, artefacts, designs and the environment, e.g. Aboriginal rock carvings or Asian lotus designs {Critical and creative thinking, Aboriginal and Torres Strait Islander histories and cultures, Asia and Australia’s engagement with Asia, Intercultural understanding} |
| identify and draw lines of symmetry on given shapes, including the special quadrilaterals and other regular and irregular shapes {Literacy} | |
| – determine and explain whether a given line through a shape is a line of symmetry {Communicating, Reasoning, Critical and creative thinking Literacy} | |
| – recognise and explain why any line through the centre of (and across) a circle is a line of symmetry {Communicating, Reasoning, Critical and creative thinking} |
Angles
ANGLES
OUTCOME
A student:
MA2-16MG: identifies, describes, compares and classifies angles
TEACHING POINTS | In Stage 2, students need informal experiences of creating, identifying and describing a range of angles. This will lead to an appreciation of the need for a formal unit to measure angles. |
| Paper folding is a quick and simple means of generating a wide range of angles for comparison and copying. | |
| The arms of the angles above are different lengths. However, the angles are the same size, as the amount of turning between the arms is the same. Students may mistakenly judge one angle to be greater in size than another on the basis of the length of the arms of the angles in the diagram. |
| LANGUAGE | Students should be able to communicate using the following language: angle, amount of turning, arm, vertex, perpendicular, right angle. |
EXPECTATIONS OF ATTAINMENT
Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) | identify ‘angles’ with two arms in practical situations, eg the angle between the arms of a clock {Critical and creative thinking} |
| identify the ‘arms’ and ‘vertex’ of an angle {Literacy} | |
| describe informally an angle as the ‘amount of turning’ between two arms | |
| – recognise that the length of the arms does not affect the size of the angle {Reasoning} | |
| compare angles directly by placing one angle on top of another and aligning one arm | |
| identify ‘perpendicular’ lines in pictures, designs and the environment {Literacy} | |
| use the term ‘right angle’ to describe the angle formed when perpendicular lines meet {Literacy} | |
| – describe examples of right angles in the environment {Communicating, Problem Solving} | |
| – identify right angles in two-dimensional shapes and three-dimensional objects {Communicating} |
Position
POSITION
OUTCOME
A student:
MA2-17MG: uses simple maps and grids to represent position and follow routes, including using compass directions
TEACHING POINTS | By convention when using grid-reference systems, such as those found on maps, the horizontal component of direction is named first, followed by the vertical component. This is a precursor to introducing coordinates on the Cartesian plane in Stage 3 Patterns and Algebra, where the horizontal coordinate is recorded first, followed by the vertical coordinate. |
| Aboriginal people use an Aboriginal land map to identify and explain the relationship of a particular Aboriginal Country to significant landmarks in the area. They use a standard map of New South Wales to identify nearby towns and their proximity to significant Aboriginal landmarks, demonstrating their unique relationship to land, Country and place. |
| LANGUAGE | Students should be able to communicate using the following language: position, location, map, plan, path, route, grid, grid reference, aerial view, directions. |
EXPECTATIONS OF ATTAINMENT
Create and interpret simple grid maps to show position and pathways (ACMMG065) | describe the location of an object using more than one descriptor, eg ‘The book is on the third shelf and second from the left’ {Literacy} |
| use given directions to follow routes on simple maps {Literacy} | |
| – use and follow positional and directional language {Communicating, Literacy} | |
| use grid references on maps to describe position, e.g. ‘The lion cage is at B3’ {Literacy} | |
| – use grid references in games {Communicating, Literacy} | |
| identify and mark particular locations on maps and plans, given their grid reference | |
| draw and label a grid on a given map | |
| – discuss the use of grids in real-world contexts, eg zoo map, map of shopping centre {Reasoning, Literacy} | |
| draw simple maps and plans from an aerial view, with and without labelling a grid, eg create a map of the classroom {Critical and creative thinking} | |
| – create simple maps and plans using digital technologies {Communicating, Information and communication technology capability} | |
| – compare different methods of identifying locations in the environment, eg compare the reference system used in Aboriginal Country maps with standard grid-referenced maps {Reasoning, Literacy, Aboriginal and Torres Strait Islander histories and cultures} | |
| draw and describe routes or paths on grid-referenced maps and plans {Literacy} | |
| – use digital technologies involving maps, position and paths {Communicating, Information and communication technology capability} | |
| interpret and use simple maps found in factual texts and in the media {Literacy} |
STATISTICS AND PROBABILITY
Data
Chance
Data
DATA
OUTCOME
A student:
MA2-18SP: selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs
TEACHING POINTS | Data could be collected from the internet, newspapers or magazines, as well as through students’ surveys, votes and questionnaires. |
| In Stage 2, students should consider the use of graphs in real-world contexts. Graphs are frequently used to persuade and/or influence the reader, and are often biased. | |
| One-to-one correspondence in a column graph means that one unit (eg 1 cm) on the vertical axis is used to represent one response/item. | |
| Categorical data can be separated into distinct groups, eg colour, gender, blood type. Numerical data has variations that are expressed as numbers, eg the heights of students in a class, the number of children in families. |
LANGUAGE | Students should be able to communicate using the following language: information, data, collect, category, display, symbol, list, table, column graph, picture graph, vertical columns, horizontal bars, equal spacing, title, key, vertical axis, horizontal axis, axes, spreadsheet. |
| Column graphs consist of vertical columns or horizontal bars. However, the term ‘bar graph’ is reserved for divided bar graphs and should not be used for a column graph with horizontal bar |
Expectations of Attainment
Identify questions or issues for categorical variables; identify data sources and plan methods of data collection and recording (ACMSP068) | recognise that data can be collected either by the user or by others {Civics and citizenship} |
| identify possible sources of data collected by others, eg newspapers, government data-collection agencies, sporting agencies, environmental groups {Literacy, Critical and creative thinking, Sustainability, Civics and citizenship} | |
| pose questions about a matter of interest to obtain information that can be recorded in categories | |
| predict and create a list of categories for efficient data collection in relation to a matter of interest, eg ‘Which breakfast cereal is the most popular with members of our class?’ {Literacy} | |
| – identify issues for data collection and refine investigations, eg ‘What if some members of our class don’t eat cereal?’ {Problem Solving, Critical and creative thinking} |
Collect data, organise it into categories, and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies(ACMSP069) | collect data and create a list or table to organise the data, eg collect data on the number of each colour of lollies in a packet |
| – use computer software to create a table to organise collected data, eg a spreadsheet {Communicating, Information and communication technology capability} | |
| construct vertical and horizontal column graphs and picture graphs that represent data using one-to-one correspondence | |
| – use grid paper to assist in constructing graphs that represent data using one-to-one correspondence {Communicating} | |
| – use the terms ‘horizontal axis’, ‘vertical axis’ and ‘axes’ appropriately when referring to column graphs {Communicating, Literacy} | |
| – use graphing software to enter data and create column graphs that represent data {Communicating, Information and communication technology capability} | |
| – mark equal spaces on axes, name and label axes, and choose appropriate titles for column graphs {Communicating, Literacy} | |
| – choose an appropriate picture or symbol for a picture graph and state the key used {Communicating} |
Interpret and compare data displays (ACMSP070) | describe and interpret information presented in simple tables, column graphs and picture graphs {Literacy} |
| – make conclusions about data presented in different data displays, eg ‘Football is the most popular sport for students in Year 3 at our school’ {Communicating, Reasoning, Literacy} | |
| represent the same data set using more than one type of display and compare the displays | |
| – discuss the advantages and/or disadvantages of different representations of the same data {Communicating, Reasoning, Critical and creative thinking} |
Chance
CHANCE
OUTCOME
A student:
MA2-19SP: describes and compares chance events in social and experimental contexts
| TEACHING POINTS | Random generators include coins, dice and spinners. |
| LANGUAGE | Students should be able to communicate using the following language: chance, experiment, outcome, random, trials, tally, expected results, actual results. |
EXPECTATIONS OF ATTAINMENT
Conduct chance experiments, identify and describe possible outcomes, and recognise variation in results (ACMSP067) | use the term ‘outcome’ to describe any possible result of a chance experiment {Literacy} |
| predict and list all possible outcomes in a chance experiment, eg list the outcomes when three pegs are randomly selected from a bag containing an equal number of pegs of two colours | |
| predict and record all possible combinations in a chance situation, eg list all possible outfits when choosing from three different T-shirts and two different pairs of shorts {Critical and creative thinking} | |
| predict the number of times each outcome should occur in a chance experiment involving a set number of trials, carry out the experiment, and compare the predicted and actual results | |
| – keep a tally and graph the results of a chance experiment {Communicating} | |
| – explain any differences between expected results and actual results in a chance experiment {Communicating, Reasoning, Critical and creative thinking} | |
| – make statements that acknowledge ‘randomness’ in a situation, eg ‘The spinner could stop on any colour’ {Communicating, Reasoning, Literacy, Critical and creative thinking} | |
| – repeat a chance experiment several times and discuss why the results vary {Communicating, Critical and creative thinking} |